anonymous one year ago Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226. -334 -274 -284 -346

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1. Michele_Laino

hint: we can write these equations: $\Large \begin{gathered} {a_{22}} = {a_1} + 21d \hfill \\ {a_{31}} = {a_1} + 30d \hfill \\ \end{gathered}$ since the general formula is: $\Large {a_n} = {a_1} + \left( {n - 1} \right)d$ where d is the constant of your sequence

2. Michele_Laino

using your data we can rewrite the first equation as follows: $\Large - 226 = 26 + 21d$ please solve that equation for d

3. anonymous

-252=21d d=-12

4. anonymous

is that right

5. Michele_Laino

that's right!

6. Michele_Laino

now, substituting that value of d into the second equation, we get: $\Large {a_{31}} = 26 + 30 \times \left( { - 12} \right) = ...?$

7. anonymous

-344

8. anonymous

Thanks!

9. Michele_Laino

that's right!

10. Michele_Laino

:)

11. anonymous

Given the functions f(n ) = 11 and g(n ) = -2(n - 1), combine them to create an arithmetic sequence, an, and solve for the 31st term. an = 11 - 2(n - 1); a31 = -49 an = 11 - 2(n - 1); a31 = -51 an = 11 + 2(n - 1); a31 = 71 an = 11 + 2(n - 1); a31 = 73

12. anonymous

can u help me with this one

13. Michele_Laino

ok!

14. Michele_Laino

for example, let's consider the first option: we have: $\Large {a_n} = 11 - 2\left( {n - 1} \right)$ so for n=31, we can rewrite that equationas follows: $\Large {a_{31}} = 11 - 2 \times \left( {31 - 1} \right) = ...?$ please continue

15. anonymous

a31= -49 right?

16. Michele_Laino

yes! that's right!

17. anonymous

Thanks

18. anonymous

Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain. n an 1 40 2 47 3 54

19. anonymous

can u help me with this one

20. anonymous

Those are the options: an = 40 + 7(n - 1) where n ≥ 40 an = 40 + 7(n - 1) where n ≥ 1 an = 40 - 7(n - 1) where n ≥ 40 an = 40 - 7(n - 1) where n ≥ 1

21. Michele_Laino

Please wait: also the third option is correct, since we can write this: $\Large {a_{31}} = 11 + 2 \times \left( {31 - 1} \right) = ...?$

22. anonymous

Oh

23. anonymous

a31=11+2×(31−1)= 71

24. Michele_Laino

yes!

25. anonymous

71 is not an answer option tho

26. anonymous

Oh yes it is nevermind

27. anonymous

Which one is the right one? How can I know?

28. Michele_Laino

I'm pondering...

29. anonymous

Do I just make a guess?

30. Michele_Laino

maybe the first one, since the first option contains both f(n) and g(n), whereas the third option contains f(n) and -g(n)

31. anonymous

Okay thanks!

32. Michele_Laino

:)

33. anonymous

can u help me with thise one now: Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain. n an 1 40 2 47 3 54 Those are the options: an = 40 + 7(n - 1) where n ≥ 40 an = 40 + 7(n - 1) where n ≥ 1 an = 40 - 7(n - 1) where n ≥ 40 an = 40 - 7(n - 1) where n ≥ 1

34. Michele_Laino

ok!

35. Michele_Laino

the constant of your sequence is: $d = 47 - 40 = 54 - 47 = ...?$

36. anonymous

d=7

37. Michele_Laino

that's right!

38. anonymous

:)

39. Michele_Laino

so, since the general formula, is: $\Large {a_n} = {a_1} + \left( {n - 1} \right)d$ replace a_1 with 40 and d with 7, what do you get?

40. anonymous

an=40+(n−1)7

41. anonymous

whats in the n spot?

42. Michele_Laino

n is the number of terms, it is a natural number, more precisely n-1 is the number of terms of the sequence which precede a_n

43. anonymous

Okay so is the answer the second one

44. Michele_Laino

yes! since we start to count from n=1

45. anonymous

THANKS!

46. Michele_Laino

:)